Let f be defined by

f(x, y) = 1 /(1 x y ), |x + y| < 1.

(a) Find the quadratic approximation of f at the origin using Taylor's formula.

(b) Evaluate(sigma notation with infinity on top and i=0 at bottom)[ E i=0 r^i] for r = x + y. Find the sum of the first three terms (sigma notation with 2 on top and i=0 down)E2 i=0[r^i] in terms of x and y.

(c) Verify that the formula in (a) and (b) are the same.